Busch's theorem for mappings

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For rotation-invariant Hamiltonian systems, canonical angular momentum is conserved. In beam optics, this statement is known as Busch's theorem. This theorem can be generalized to symplectic mappings; two generalizations are presented in this paper. The first one states that a group of rotation-invariant mappings is identical to a group of the angular-momentum preserving mappings, assuming both of them symplectic and linear. The second generalization of Busch's theorem claims that for any beam which rotation symmetry happened to be preserved, an absolute value of the angular momentum of any particle from this beam is preserved as well; the linear symplectic mapping ... continued below

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53 Kilobytes pages

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Burov, A. May 29, 2001.

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For rotation-invariant Hamiltonian systems, canonical angular momentum is conserved. In beam optics, this statement is known as Busch's theorem. This theorem can be generalized to symplectic mappings; two generalizations are presented in this paper. The first one states that a group of rotation-invariant mappings is identical to a group of the angular-momentum preserving mappings, assuming both of them symplectic and linear. The second generalization of Busch's theorem claims that for any beam which rotation symmetry happened to be preserved, an absolute value of the angular momentum of any particle from this beam is preserved as well; the linear symplectic mapping does not have to be rotation-invariant here.

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53 Kilobytes pages

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  • PAC 2001, Chicago, IL (US), 06/2001

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  • Report No.: FERMILAB-Conf-01-074-T
  • Grant Number: AC02-76CH03000
  • Office of Scientific & Technical Information Report Number: 781160
  • Archival Resource Key: ark:/67531/metadc715634

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  • May 29, 2001

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  • Sept. 29, 2015, 5:31 a.m.

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  • April 1, 2016, 5:17 p.m.

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Burov, A. Busch's theorem for mappings, article, May 29, 2001; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc715634/: accessed September 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.